3.1 Ts sources (MGRsD, MGRsD_TAIR, From paper, Rs_Ts_relationship)

First, we tested the effect of different soil temperature sources on the Rs_annual_bahn vs Rs_annual relationship:

• From MGRsD means mean annual soil temperature (amst) are from a global monthly soil respiration database, each site has more than 12 months measured soil temperature read from original papers.
• From paper means amst were reported from the original paper (table, figures, or description).
• Partly from TAIR means: some studies did not measure soil temperature all year, for those months, we predict soil temperature based on monthly air temperature (Tsoil = 2.918 + 0.829xTair). This model was developed based on the sites which have >= 12 months soil temperature measurements.
• There are 67 records for which I cannot get the soil temperature information through the above three methods. In these cases, based on the Rs_Ts_relationship and reported Rs_annual, I calculated the amst.
• The calculated amst was then compared with the annual Tair, if they are well matched (error < 5%), calculated mast were used.
• When calculated amst and annual Tair do not match, this usually indicates a potential problem, and then I went back to the manuscript and checked.
• Whenever a paper reported annual mean Ts, I compared the reported mast and estimated mast based on the Rs_Ts_relationship, and found they are well matched.

Generally, Ts sources do not have clear effects on the Rs_annual_bahn and Rs_annual relationship.

3.2 Annual Rs or Ts coverage effect

Second, we tested whether Ts and Rs coverage (e.g., 0-0.5 means Rs or Ts only measured less than 6 months, versus the entire year), but found that Ts and Rs coverage do not have significant effects on the Rs_annual_bahn vs Rs_annual relationship.

3.3 Effect of maximum allowed divergence between global climate data set and site-specific air temperature

Third, we tested whether maximum allowed divergence between global climate data set and site-specific air temperature affect the Rs_annual_bahn vs Rs_annual relationship.

As we throw out data points with high divergence, R2 and RSE go up and down inconsistently and by small amounts, suggesting that the Tair divergence do not have a consistent effect.

3.4 Effect of maximum allowed divergence between annual precipitation from paper and Del

Fourth, we also tested whether the maximum allowed divergence between the global climate data set and site-specific precipitation affects the Rs_annual_bahn vs Rs_annual relationship. In other words, does a bias in the global data affect things?

As we throw out data points with high divergence, R2 and RSE showed no large or consistent changes, suggesting that the precipitation divergence does not have a large effect.

We also compared:

• MAT from U. Delaware (MAT_Del) and MAT reported from the papers (a)

• TAnnual from U. Delaware (TAnnual_Del) and annual temperature from papers (study_temp) (b)

• MAP from U. Delaware (MAP_Del) and MAP reported from the papers (c)

• PAnnual from U. Delaware (PAnnual_Del) and annual precipitation from papers (study_precip) (d)

In general, the temperature and precipitation from the University of Delaware climate data matched the data reported from publications well. This supports the idea that the divergence between global climate data set and site-specific precipitation/temperature has little to no effect.

We tested the effect of precipitation and temperature variability [quantified by the standard deviation of annual mean air temperature (amat) between 1964 and 2017, and annual precipitation deviation between 1964 and 2017], using multiple linear regression, with divergence as catergorical indicator. We found that they have no significant effect on the Rs_annual_bahn vs Rs_annual relationship.

3.5 Test ecosystem type

The Rs_annual_ban vs Rs_annual relationship varies among different ecosystems.

• For example, agriculture has lower slope but wetland has higher slope.

• However, it is unlikely that the data from agriculture and wetland shift the overall regression between Rs_annual_bahn vs Rs_annual away from 1:1 line.

• When we remove the Ag data, the Rs_annual_bahn vs Rs_annual regression still differs from 1:1 line.

• When we plot Ag alone, we see the Rs_annual_bahn vs Rs_annual regression in Ag does not greatly differ from the rest.

• We also examined the influential outlier points (cooks.distance > 0.5). When the outliers were removed, the regression showed no difference, indicating that outliers do not have large effects.

• Similar conclusion for wetland data.

3.6 Test Rs measurement method

Different measurement methods do not affect the Rs_annual_bahn vs Rs_annual relationship.

3.7 RA- or RH-dominated effect?

A particularly interesting question is whether the Rs_annual_bahn vs Rs_annual relationship changes in sites dominated by autotrophic (RA) or heterotrophic (RH) respiration. This might be the case if, for example, one respiration source had a consistently highly temperature sensitivity.

• RA dominated sites tend to have larger intercept than RH dominated sites, but no difference in slope.

We tested Q10 (temperature sensitivity) and R10 (Rs at a standardized 10 C) at RA and RH-dominated sites.

• RA dominated sites have larger Q10 (over the 0-10, 5-10, 10-20, and 0-20 soil temperature ranges) values and R10 values.

3.8 Biome effect?

• ‘Mediterranean’ sites exhibit large differences from other biomes.

3.9 Drought effect?

In their paper, Bahn et al. (2010) reported that drought stress significantly affected the relationship. Using our new datasets we found that:

• MAP effects on the Rs_annual_bahn vs Rs_annual relationship is very limited (p ~~ 0.05).
• The slope and intercept changes do not followed a clear pattern as MAP changes.
• MAP is not a good drought index.

We then tested standardized drought index (SPI).

• SPI significantly affects Rs_annual_bahn vs Rs_annual relationship; as SPI decreases, the slope decreases, means the Bahn approach tends to overestimate Rs_annual under drought condition.

Since SPI compares annual precipitation at a site with average precipitation over a period (we used 1964-2014), it can not describe spatial drought in drought.

We thus also used another drought index, the Palmer Drought Severity Index (PDSI), to characterize spatial effects.

• PDSI significantly affects the Rs_annual_bahn vs Rs_annual relationship: as it becomes drier, the slope tend to decrease, meaning that the Bahn method overpredicts the annual flux. This is consistent with the SPI finding above.

4.2 Predicting Rs_annual from air temperatures

Since high resolution soil temperature is still lacking, and/or has lower accuracy than air temperature data, we want to test whether we can use Rs at annual mean air temperature (amat) or mean annual temperature (mat) to predict Rs_annual.

• The regression between Rs_annual_bahn_amat and Rs_annual falls away from the 1:1 line, with an intercept significantly different from 0 (p<0.001) and slope significantly different from 1 (p<0.001).
• Note that we tested both new_model1 and new_model2 models.
• Using amat or mat show no big difference, but it is surprising that using mat is slightly better than using amat.

We detected 2 outliers in the Rs_annual_bahn vs Rs_annual regression. * Remove these two outliers significantly improved the model (slope changed from 0.78 to 0.87, intercept decreased from 222 to 157, however, p values for slope and intercept are still < 0.001).

• The results showed that we cannot directly using Rs_amat or Rs_mat to predict Rs_annual because the bahn(2010), new_model1, and new_model2 are based on Rs_amst to predict Rs_annual.
• Based on the relationship between Ts and Tair (i.e., Ts = 2.918+0.829*Tair), we adjusted amat and mat
• amat_adj = 2.918 + 0.829 x amat, mat_adj = 2.918 + 0.829 x mat, and applied amat_adj and mat_adj to new_model2
• The results are better, but still not resolve the problem (p<0.05)

4.3 Re-simulate a model (new_model3)

We thus re-calculated soil respiration at annual mean air temperature (Rs_amat, i.e., using air temperature rather than soil temperature to calculate soil respiration).

• Then we re-simulated the relationship between Rs_annual and Rs_amat.
• Rs_annual = 729.09225 * (Rs_amat ^ 0.46535) + 89.7789 * spi – Medeterrean
• Rs_annual = 588.618 * ( Rs_amat ^ 0.65022 ) + 22.59026 * spi + 11.29775*pdsi – exclude Mediterranean sites
• If we update the model, Rs_annual_bahn_amat can represent Rs_annual.

• Comparing Rs_annual and Rs_annual_bahn by different models, the results showed that directly using Bahn(2010) model does not well represent Rs_annual (slope=0.75, p<0.001, intercept=164, p<0.001).
  

• However, the updated new_model1, new_model2, and new_model3 well represent Rs_annual (p>0.05 for slope).

• Using Rs measured at mean air temperature can also well represent Rs_annual (new_model3).

• report model stats/parameters

Wed Apr 17 13:35:21 2019 ——————————————-

Call: lm(formula = Rs_annual ~ Rs_bahn, data = sdata)

Residuals: Min 1Q Median 3Q Max -779.97 -111.55 -38.28 84.77 1264.91

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 156.42544 13.24599 11.81 <2e-16 Rs_bahn 0.76142 0.01302 58.50 <2e-16 — Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1

Residual standard error: 193.9 on 821 degrees of freedom Multiple R-squared: 0.8065, Adjusted R-squared: 0.8063 F-statistic: 3422 on 1 and 821 DF, p-value: < 2.2e-16

[1] “——————————————-Test whether intercept differ from 1” [1] “t_slope = 18.329, p_slope = 0, df = 821” Wed Apr 17 13:35:21 2019 ——————————————-

Call: lm(formula = Rs_annual ~ Rs_bahn, data = sdata)

Residuals: Min 1Q Median 3Q Max -666.34 -113.06 -34.00 79.66 1254.42

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.6951 15.3287 2.002 0.0456 *
Rs_bahn 0.9699 0.0168 57.724 <2e-16 *** — Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1

Residual standard error: 196 on 821 degrees of freedom Multiple R-squared: 0.8023, Adjusted R-squared: 0.8021 F-statistic: 3332 on 1 and 821 DF, p-value: < 2.2e-16

[1] “——————————————-Test whether intercept differ from 1” [1] “t_slope = 1.792, p_slope = 0.074, df = 821” Wed Apr 17 13:35:21 2019 ——————————————-

Call: lm(formula = Rs_annual ~ Rs_bahn, data = sdata)

Residuals: Min 1Q Median 3Q Max -700.54 -112.70 -37.46 80.85 1226.84

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.61176 15.09381 2.028 0.0429 *
Rs_bahn 0.97000 0.01653 58.664 <2e-16 *** — Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1

Residual standard error: 193.5 on 821 degrees of freedom Multiple R-squared: 0.8074, Adjusted R-squared: 0.8072 F-statistic: 3441 on 1 and 821 DF, p-value: < 2.2e-16

[1] “——————————————-Test whether intercept differ from 1” [1] “t_slope = 1.814, p_slope = 0.07, df = 821” Wed Apr 17 13:35:21 2019 ——————————————-

Call: lm(formula = Rs_annual ~ Rs_bahn, data = sdata)

Residuals: Min 1Q Median 3Q Max -1649.36 -153.12 -47.84 111.84 2238.55

Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.66486 23.48793 0.199 0.843
Rs_bahn 0.99521 0.02626 37.905 <2e-16 *** — Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1

Residual standard error: 265.8 on 821 degrees of freedom Multiple R-squared: 0.6364, Adjusted R-squared: 0.6359 F-statistic: 1437 on 1 and 821 DF, p-value: < 2.2e-16

[1] “——————————————-Test whether intercept differ from 1” [1] “t_slope = 0.183, p_slope = 0.855, df = 821”

Model parameters and statistic summary

var_model	intercept	t_inter	p_inter	slope	t_slope	p_slope
Bahn(2010)	156.425	11.809	0.000	0.761	18.329	0.000
new_model1	30.695	2.002	0.046	0.970	1.792	0.074
new_model2	30.612	2.028	0.043	0.970	1.814	0.070
new_model3	4.665	0.199	0.842	0.995	0.183	0.855